Online+Game+-+Geometry

** LESSON PLAN **
**(Created by: Andrea Handler-Ruiz, Nov 2010)**

**Lesson Focus (On-line game/interactive based)** ** Applying applets to measure areas of simple geometric shapes, and determine relationships between shapes. Concepts are reinforced through a board game manipulative that relates the area of a square to a rectangle; a manipulative that relates the area of a rectangle to the area of triangles; a manipulative that relates a parallelogram to a rectangle. **

**Content Objective** Students will be able to relate the areas of a rectangle, a parallelogram, and a triangle using applets and by doing paper manipulative activities. Students will be able to find the area of a triangle using the area of a parallelogram. Students will be able to find the area of a parallelogram using the area of a rectangle.

Students will be able to define vocabulary terms and use them in explanations. Students will be able to discuss problem solving strategies using words and symbols. Students will express an opinion by constructing paragraphs.
 * Language Objective **

segment, length, area, rectangle, parallelogram, triangle, square, conjecture, congruent, rotation, reflection, vertices, formula
 * Key Vocabulary **

**Cultural Objectives** ** Students will be able to asses and discuss their comfort level on using technology to learn. **

**Overview Lesson Strategy** Students will use a virtual interactive tool to solve for areas, comparing shape relationships by using a simulation. Students will use traditional methods of solving for areas, comparing shape relationships by manipulating paper shapes. Students will use a Venn diagram to compare both strategies. Students will write an opinion statement on using technology as a learning strategy.


 * Lesson Sequence **
 * 1)  Access [] to work with applets that can be manipulated to calculate areas and show relationships between a rectangle, a parallelogram, and a triangle. The student will be able to interact with the shapes show on the screen and explore their relationships at his/her own pace.
 * 2) Determining Areas: Start by working with the __Area of a Rectangle__. Students should follow instructions to drag the indicated points to change the dimension of the rectangle. Some points can be displaced, others are fixed. As the points are dragged the rectangle increases in length or in height, changing its overall dimensions. As this happens, the value of the segment lengths displayed and the area of the figure also changes. Students should be asked to verify the given area by calculating it by hand and by using a calculator. Let students explore different dimensions and tabulate their findings in a table. They should include at least five different set of dimensions and their corresponding areas. Click on Exploration for students to read about how the formula to calculate the area of a rectangle is derived and how it related to a square. Have students explain this process to each other by drawing different size rectangles on graph paper and highlighting the number of squares that it includes.
 * 3) Determining Areas: Click on __Area of a Parallelogram__ to explore how a rectangle relates to a parallelogram. Certain points can be dragged to change the shape and area of the parallelogram. In this applet, the parallelogram is divided into two triangle pieces; clicking on a specific point allows the student to drag half of the parallelogram to create a rectangle. Have students make a conjecture as to how the area of the parallelogram can be calculated once a rectangle is made and corroborate if this is true for parallelograms of different sizes. Also, have students discuss if all parallelograms have the same area? (These questions are stated in the Exploration tab).
 * 4) Determining Areas: Return to the main page of the site and click on __Area of a Triangle__. Allow students to explore the shape by dragging the points and changing its dimensions. Students can make a copy of the triangle, rotate and drag it to form a parallelogram and determine what dimensions need to be known to calculate its area. Students should be able to tell you what known shape is formed without the teacher telling them. This should be answered before going on the Exploration phase of the applet where the student is asked to relate a triangle to a parallelogram. At the end, students should be able to discuss with confidence: What measurements on the triangle do you need to know in order to find the area of a parallelogram? How can you calculate the area of a triangle?
 * 5) Board Game (team activity): To reinforce the concept that squares can be used to form rectangles have students do the following activity to determine the most number of ways to connect five squares edge to edge. Have a visual representation available, and possibly model a possible arrangement of squares for students that may need extra help visualizing the game set-up:

a. Cut five squares of similar dimensions drawn on graph paper.

b. Arrange the squares edge to edge in as many ways as possible. Do not include any congruent figures. If a figure is a rotation or a reflection of one of the other figures, it is a congruent figure.

c. Draw a picture of each figure on graph paper. Each team receives a point for each figure it finds. A team loses a point if they have congruent figures or they have a figure in which the squares are not arranged edge to edge. The teacher will determine the time allotted for this phase of the game.

d. Alternative approach: After teams have found all of the possible figures, cut out the drawings and arrange them so that they fit together as a large rectangle. Calculate the area by: 1) counting the number of squares and multiplying by the area of each square, 2) Using the formula to determine the area of a rectangle. The team that finishes first correctly wins the game.

6. Manipulative (individual or pairs): To reinforce the concept that the area of a rectangle can be determined using the are of triangles, have students do the following activity: a. Begin by posting a Focus Question: How do you find the area of a triangle? Students should be guided to state the formula. Write it down on the board for reference. Proceed to explore with drawings and paper triangles. b. Have students draw on a graph paper a large triangle, which they should color and enclose within a rectangle. Label the two smaller triangles formed on either side of the large triangle, A and B. Have students measure the dimensions of the rectangle using a ruler and calculate its area using the corresponding formula. Write this down. c. Cut out the rectangle and then the triangles. Students will end up with a large colored triangle and two smaller triangles, A and B. d. Cover the large triangle with the two smaller triangles. Tape the pieces forming flaps. e. Discuss the following questions: - Do the two smaller triangles cover the same area as the large triangle? - How is the area of the large triangle related to the area of the original rectangle? - Have students determine and write a rule for finding the area of a triangle given its base equals the base of the rectangle and its height equals the height of the rectangle. - Use the area of the rectangle to find the area of the large triangle. - Have students calculate the area of all three triangles and determine how they relate to each other and to the original rectangle.

7. Manipulative (Individual): To reinforce the relationship between the area of a parallelogram and a rectangle, have students do the following activity using an index card: a. Have students measure the length and width of an index card and discuss the appropriate formulate to calculate its area. Write this down. b. Have students draw a line through one of the vertices of the index card. c. Cut out the triangle that is formed. d. Tape the triangle cut-out to the opposite side to form a parallelogram. e. Students should discuss and answer the following questions: - How does the area of a parallelogram compare to the area of the rectangular index card? - How do the bases compare? - How do their heights compare? - Write a conjecture about the formula for the area of a parallelogram.

8. Venn diagram: Close the lesson by having students brainstorm on the pros and cons of using technology to aid their understanding of the relationship between the areas of a square, rectangle, a parallelogram, and a triangle. Guide the discussion and the inclusion of the summary points in a class Venn diagram. Each student should then write an individual opinion (1-2 paragraphs) on using technology (applets) or paper manipulative activities to decipher meaning and learn math concepts.

This lesson will provide students with opportunities to use art and perspectives of two and three dimensional shapes in conjunction with language skills to discuss math concepts.
 * Interdisciplinary Connections **

** High School Geometry standards: Use properties and characteristics of two- and three dimensional shapes and geometric patterns to describe relationships, communicate ideas, and solve problems. **
 * CSDE Standards and Performances **

2-3 days, according to student level
 * Approximate Timeframe **

**Assessments** Student progress and achievement will be evaluated by analyzing their: 1. Table - Area of Rectangles, and graph paper drawings of squares and rectangles. 2. Verbal explanation to peers on how the formula to calculate the area of a rectangle relates to a square. 3. Participation in the discussion and forming a conjecture related to calculating the area of a parallelogram; the relationship between triangles and parallelograms and their formulas. 4. Board game engagement, group contribution, and completion. 5. Completed manipulative on finding the area of a triangle, and related discussion questions and calculations. 6. Completed manipulative on exploring the area of a parallelogram using an index card, and related discussion, questions and calculations. 7. Copying of class derived Venn diagram and individual position statement on using technology as a learning tool.

If computers malfunction or the Internet site is not available due to accessibility restrictions, the teacher can provide verbal instructions for students to draw the different representations of the geometric figures and use elastics, string, or straws to guide the virtual game part of the lesson. In lieu of this alternative, the teacher can just skip to the other sections of the lesson that do not require Internet access.
 * Contingency Plan: **

The use of video games, on-line games, and interactive tools can be a powerful tool to engage students and promote learning. Creative problem solving through video gaming or on-line manipulative games can become an additional strategy to be used by the teacher to enhance learning via an immersion approach. Through simulated interactions students are required to produce a result as a critical player: without their moves the outcome will not be the same, therefore their input is very important. Including a section of a lesson using this alternative strategy is fast becoming a mechanism to construct stronger classrooms, requiring students to adopt higher critical thinking skills while learning.
 * Explanation/Reflection **